African Journal of Mathematics and Mathematical Sciences ISSN: 3821-435x Vol. 2 (1), pp. 023-037, January, 2014. © International Scholars Journals
Full Length Research Paper
Christ-Obimba tangent, permutation, sequence and series rules in Calculus
Obimba Kelechukwu Clarence
Department of Biochemistry, School of Science, Federal University of Technology Owerri, P.M.B. 1526, Owerri. Nigeria. E-mail: [email protected]; Tel. 07034851899
Accepted 02 January, 2014
Abstract
The aim of this study is to develop a convenient Tangent rule that could be used for determining the area and lengths of sides of a triangle, and also to develop differentiation and integral calculus rules/formulae based on permutation and geometric progression. Christ-Obimba Calculus Rule 1 could be used in determining further/higher derivatives of a function, directly from the parent function, without recourse to the consecutive, previous derivative. For any triangle ( ) ABC,
, , and .
a, b, and c are lengths of the sides of the triangle( ) ABC (Christ-Obimba Tangent Rules).
known as Christ-Obimba Calculus Rules 1 and 2, respectively, could be used in calculus of differentiation, for determining derivatives, and further derivatives of mathematical functions. Parent /root mathematical functions, their consecutive derivatives, and further/higher derivatives, form the Christ-Obimba geometric progression sequence in calculus, given by :
The Christ-Obimba geometric progression series in calculus could be used to obtain all the derivatives, of the parent function of a finite series, without calculating individual derivatives, singly.
m = the specific derivative (1st, or 2nd or 3rd…….or mth derivative).
n = index power to which the variable x is raised. e.g : x4 (n = 4).
a = constant = coefficient of the variable term in xn.
C = constant.
T1 =the first term of the geometric progression series of calculus = axn.
Ti = the dependent variable y; Td = the term in the independent variable x.
Key Words: Tangent, calculus, permutation, geometric progression series, derivatives.